The problem with biased noise/DC offset exists in, among others, homodyne receivers that convert radio frequency signal directly into base band signal. Various factors such as components mismatch, local oscillator leakage and interferences may contribute to this distortion. When the modulation of the transmitted signal consists of a rotation operation, for example in GSM/EDGE systems, the DC offset will causes a single frequency trend in the received signal after de-rotation (demodulation). If this frequency trend is left uncompensated, the DC offset can cause significant receiver performance degradation.
Several methods are known and are currently used for compensation of the DC offset.
One such known method is blind DC estimation. This is the simplest and most straightforward method. The received signal is averaged before de-rotation. When this is applied to TDMA systems which have limited symbols in a burst, this method is not accurate due to uncertainty of the data symbols in the transmission.
Another such known method is joint channel and DC estimation. This is used when the DC offset has been treated as an extra tap in the multi-tap channel estimation, utilising the constellation rotation as a reference, for example the π/2 rotation in GSM and the 3π/8 rotation in the EDGE modulation. It has been observed, however, that the performance of this method depends on the training sequence used. It does not perform well when a training sequence has high amplitude at the trend frequency. Further, the accuracy of channel estimation is compromised due to the fact that an extra parameter needs to be estimated with the same training sequence. In addition, the performance is also affected by the form of burst synchronisation.
A further known method is referred to as classical trend elimination as disclosed for example in “System Modelling and Identification”; R. Johansson, in particular pages 83 to 85, pages 126 and 127 and pages 464 and 465. This is a method in system identification. When a stimulating sequence {tk} of length n is applied to a linear system with m parameters, a system response {xk} of length n is collected for the system identification. Trend elimination modifies the system model where neutralized sequences are used for both stimulus and observation. The neutralized sequence of the stimulus sk and the neutralized sequence of the observation (input signal) yk are derived as follows:
            s      k        =                            t          k                -                  τ          ⁢                                          ⁢          τ                    =                        1          n                ⁢                              ∑                          i              =              0                                      n              -              1                                ⁢                                          ⁢                      t            i                                          y      k        =                            x          k                -                  ρ          ⁢                                          ⁢          ρ                    =                        1          n                ⁢                              ∑                          i              =              0                                      n              -              1                                ⁢                                          ⁢                      x            i                              
This method, however, can be employed only if either the training sequence, the stimulus, is significantly longer than the model order n>>m, or just a single parameter is sufficient for system identification. It cannot be applied in a digital communication system where a multi-path channel is required to be estimated with a limited training sequence.